How do I change the name that appears in the email notification of a cloned form?

For Example:  I cloned form-1 and renamed it form-2.  When I receive submissions from form-2, they reference form-1.  How can I get my submission to reflect that they are from form-2?

I think this is because you have added the name as static text in the email notification of the first form, because it has by default the form's name, but it is a variable, it means that the name in the email notification will change as soon as you change the name of the form in the Form Builder, I would suggest you to check the email notification, to do that you only need to click on the email icon in the Form Builder, you will find it on the top toolbar: 

Click on edit in the email that you are receiving. 

Click on Edit Email and you will get a window with the content that you receive in the email notification, there you will be able to replace the current text on it. 

Other way, and the easiest, it is deleting the current email template and re-doing it, doing this you will get the fresh data of your form, this guide will help you to delete the email notification: http://www.jotform.com/help/132-How-to-Delete-Notifications-Autoresponder. 

This guide will help you to add the notification again: http://www.jotform.com/help/25-Setting-Up-Email-Notifications. 

Hope this helps. 

Worked perfectly!  Thank you so much!

On behalf of my colleague, you are most welcome. Feel free to contact us again if you have any other concerns. Cheers.